Question

One end of a nylon rope of length $4.5m$ and diameter $6mm$ is fixed to a free limb. A monkey weighting $100N$ jumps to catch the free end and stays there. Find the elongation of the rope, (Given Young's modulus of nylon $=4.8\times {10}^{11}N{m}^{-2}$ and Poisson's ratio of nylon $=0.2$)

• A. $0.332\mu m$
• B. $0.151\mu m$
• C. $0.625\mu m$
• D. $0.425\mu m$

Answer 1

The correct option is A $0.332\mu m$

Here, $=4.5m,D=6mm=6\times {10}^{-3}m,F=100N,Y=4.8\times {10}^{11}N{m}^{-2},\sigma =0.2$
As $Y=\frac{F}{A}\frac{l}{\Delta l}$
$\therefore \Delta l=\frac{F}{A}\frac{l}{Y}=\frac{100\times 4.5}{3.14\times {(3\times {10}^{-3})}^2\times 4.8\times {10}^{11}}=3.32\times {10}^{-5}m$